A pilot checks her instruments and finds that her airspeed is 345 km/h and that she is heading in a direction [S40ºW].  A radio report tells her that the wind velocity is 85 km/h [NW].  What is the velocity of her plane relative to the ground?

I tried to draw this out, but I think i did it wrong. I also tried to break it into vector components, but I am not understanding

1 answer

the plane is moving inside an air mass that is moving relative to the ground

the ground speed is the sum (vector) of the two speeds

345 kph, S40ºW
... 345 cos(40º) S
... 345 sin(40º) W

85 kph, NW
... 85 cos(45º) N
... 85 sin(45º) W

find the vector sum of the 4 components